Overview
- Group
- SmallGroup(1248,1451)
- Rank
- 5
- Schläfli Type
- {2,26,6,2}
- Vertices, edges, …
- 2, 26, 78, 6, 2
- Order of s0s1s2s3s4
- 78
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
6-fold
13-fold
26-fold
39-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4,15)( 5,14)( 6,13)( 7,12)( 8,11)( 9,10)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)(43,54)(44,53)(45,52)(46,51)(47,50)(48,49)(56,67)(57,66)(58,65)(59,64)(60,63)(61,62)(69,80)(70,79)(71,78)(72,77)(73,76)(74,75);; s2 := ( 3, 4)( 5,15)( 6,14)( 7,13)( 8,12)( 9,11)(16,30)(17,29)(18,41)(19,40)(20,39)(21,38)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(42,43)(44,54)(45,53)(46,52)(47,51)(48,50)(55,69)(56,68)(57,80)(58,79)(59,78)(60,77)(61,76)(62,75)(63,74)(64,73)(65,72)(66,71)(67,70);; s3 := ( 3,55)( 4,56)( 5,57)( 6,58)( 7,59)( 8,60)( 9,61)(10,62)(11,63)(12,64)(13,65)(14,66)(15,67)(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52)(27,53)(28,54)(29,68)(30,69)(31,70)(32,71)(33,72)(34,73)(35,74)(36,75)(37,76)(38,77)(39,78)(40,79)(41,80);; s4 := (81,82);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(82)!(1,2); s1 := Sym(82)!( 4,15)( 5,14)( 6,13)( 7,12)( 8,11)( 9,10)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)(43,54)(44,53)(45,52)(46,51)(47,50)(48,49)(56,67)(57,66)(58,65)(59,64)(60,63)(61,62)(69,80)(70,79)(71,78)(72,77)(73,76)(74,75); s2 := Sym(82)!( 3, 4)( 5,15)( 6,14)( 7,13)( 8,12)( 9,11)(16,30)(17,29)(18,41)(19,40)(20,39)(21,38)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(42,43)(44,54)(45,53)(46,52)(47,51)(48,50)(55,69)(56,68)(57,80)(58,79)(59,78)(60,77)(61,76)(62,75)(63,74)(64,73)(65,72)(66,71)(67,70); s3 := Sym(82)!( 3,55)( 4,56)( 5,57)( 6,58)( 7,59)( 8,60)( 9,61)(10,62)(11,63)(12,64)(13,65)(14,66)(15,67)(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52)(27,53)(28,54)(29,68)(30,69)(31,70)(32,71)(33,72)(34,73)(35,74)(36,75)(37,76)(38,77)(39,78)(40,79)(41,80); s4 := Sym(82)!(81,82); poly := sub<Sym(82)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;